Junior high school mathematics guidance, taking junior high school mathematics syllabus as the criterion, aims at learning junior high school mathematics knowledge, developing thinking and improving ability, and tests the learning effect through the senior high school entrance examination. This paper analyzes what knowledge students should learn, what methods and skills they should master and what ability requirements they should meet in different learning periods, and gives hierarchical teaching guidance according to different ability levels.
Keywords: time knowledge ability level
The research object of mathematics is the relationship between spatial form and quantity. Hua, a famous mathematician, once said: "The number of missing shapes is less intuitive, and the number of shapes is difficult to be nuanced." In contemporary society, the application of mathematics is more and more extensive. It is an indispensable tool for people to participate in social life, engage in productive labor and study, and learn modern science and technology. Its contents, ideas, methods and language have been widely infiltrated into natural science and social science and become an important part of modern culture.
Junior high school mathematics is a major subject of compulsory education. It is the basis of studying physics, chemistry, computer and other subjects, participating in social life, production and further study, and has a positive effect on the formation of students' good personality and dialectical materialist world outlook. Therefore, it is very necessary for students to receive the necessary mathematics education and have certain mathematics literacy, so as to improve the quality of the whole nation and lay the foundation for cultivating talents for socialist construction. ?
Teaching purpose:
The purpose of junior high school mathematics teaching is to enable students to learn the basic knowledge and skills of algebra and geometry necessary for every citizen in contemporary society to adapt to daily life, participate in production and further study, further cultivate their computing ability, develop their thinking ability and spatial concept, enable them to solve simple practical problems with what they have learned, and gradually form a sense of mathematical innovation. Cultivate students' good personality and preliminary dialectical materialism.
According to the chronological order of teaching:
Learning in Grade One is particularly important. On the basis of primary school study, we began the process from number letters, from letters to algebraic expressions, to the formation and deepening of equations.
Throughout the teaching content of senior one, it is mainly to learn and understand concepts and definitions; Skillfully and accurately operate rational numbers, algebraic expressions and equations; Understand the research elements of geometry (point, line, surface, angle, body, etc.). ). Computing ability The ability that first-year students must master, only through calculation can they learn more advanced knowledge better.
Let's look at a teaching example: Zhao, a junior one student at Beijing Chaoyang Foreign Language School. He is introverted and inarticulate. Generally speaking, the main problem of the upper level in mathematics is that his calculation ability is not enough, and he often loses points unnecessarily in calculation. When I first met him, I could see that he was more relaxed and indifferent to mathematics learning. It is this blind self-confidence that makes his calculation accuracy not high and his comprehensive score can't come up. After the first class, I basically found out Zhao's problem. I made a plan for Zhao, as follows:
1. Go home and check the wrong calculation in the previous homework, test questions and exercise books to find out the wrong reasons;
2. Finish our homework carefully after class, review the learning content in class, and extract the wrong questions into the wrong book;
3. First, let him realize the seriousness of arithmetic mistakes in class, and he can completely overcome carelessness through hard work;
4. From the operation rules and algorithms to the standardization of operation steps, methods and skills, the teaching effect is tested through test questions.
In the mid-term exam, Zhao's math score was 1 15 (only one additional question was not completed). To sum up the teaching of operational research, it is mainly to attach importance to operational research and understand its logic with a mentality; You can seek and design a reasonable and simple operation mode according to the problem.
The improvement of scores is the best gift for students. When we stimulate students' enthusiasm for learning, master the knowledge in class and improve students' understanding and application ability, it is natural.
The second day of junior high school is the period when students are most likely to fall behind. Starting from the subject of mathematics alone, the second day of junior high school began to formally contact with the problem of geometric proof and learning function. These two knowledge require students to master good spatial imagination, construction ability and functional thinking. The key to junior high school geometry problems is to "add auxiliary lines" and cultivate the concept of space.
Here we also give a concrete teaching example: He Laoshi is a junior two student in Beijing Sanfan Middle School. According to reports, his math scores in Grade One are among the best in his class. When I studied the chapter of isosceles triangle, I had no idea about adding auxiliary lines. I studied hard and memorized the basic concepts and theorems, but my grades were not as good as before. When we met, we could see from his eyes his thirst for knowledge and his trust in me.
For He Laoshi's tutoring,
1. Let him observe specific things, such as tables, rooms, trinkets, etc., starting from the chapter on graphics in Chapter 4. , and then observe the structure of plane graphics and three-dimensional graphics (points, lines, edges, corners, etc.). );
2. Then transition to Chapter 7 Triangle. At this time, students are required to draw geometric figures (triangle, three lines of triangle, etc.). ), and expand and restore three-dimensional graphics;
3. When learning isosceles triangle, emphasize the importance of axial symmetry with students, especially when adding auxiliary lines;
4. Introduce the basic geometric models: angle bisector model, adjacent equilateral model, double angle model, etc.
5. Do special exercises, analyze the process of adding auxiliary lines, and analyze the training of multiple solutions to one question, multiple solutions to one question and multiple solutions to one question. Need to observe and ponder repeatedly;
After just five classes, He Laoshi not only overcame the geometry problem, but also increased his enthusiasm for learning geometry. Now I have learned quadrilateral, so I am relaxed and devoted. For geometry, it is particularly important to cultivate the ability of spatial imagination. I can draw skillfully, and all the problems can be solved easily.
Summarize the teaching of geometry: it can cultivate students' spatial imagination ability, simple objects in life can imagine geometric figures, and the shape of objects can be imagined from geometric figures; Can separate simple and basic graphics from more complex plane graphics; Be able to find out the basic elements and their relationships in basic graphics; Be able to make or draw graphics according to conditions.
For the students in grade three, it is mainly to form comprehensive ability, adjust their mentality and actively face their study and life.
According to the textbook arrangement, the knowledge learned in senior three needs to be decompressed in the senior high school entrance examination. But most schools will finish the new course in the last semester of the third grade. So for the guidance of grade three, we have three rounds of review.
The first round: the winter vacation of the third semester is very important. Arrange the winter vacation time reasonably, and students with weak foundation begin to review the foundation to make up for their weak places; Students with good academic qualifications should start to cultivate their comprehensive ability as soon as possible and form their comprehensive ability.
The second round: before the start of the new semester, students of all levels should follow the school for a unified basic review, take teaching time as the horizontal axis, read the textbooks carefully, be familiar with the knowledge distribution of the textbooks, and master the knowledge difficulties, key points, problem-solving methods and skills of each chapter skillfully. According to the vertical axis of knowledge structure and depth, this paper summarizes the common characteristics and differences of related knowledge, as well as the comprehensive application methods of related chapters.
The third round: after the second model, check for leaks and fill gaps, form comprehensive ability, return to textbooks, summarize the knowledge and ability of the previous paragraph, analyze the shortcomings of the previous paragraph, and further supplement and improve it.
In the whole teaching process of grade three, we should pay attention to adjusting students' psychology, actively facing learning and life and promoting learning.
The innovative consciousness to be cultivated in junior middle school mathematics mainly refers to: being curious about the phenomena in nature and society, constantly pursuing new knowledge and independent thinking, finding and putting forward problems from the perspective of mathematics, and exploring, studying and solving problems with mathematical methods.
In mathematics teaching, developing thinking ability is the core of cultivating ability. In the new era, as a teacher, we should not only cultivate students' mathematical knowledge, but also cultivate their innovative consciousness, stimulate their interest, confidence and perseverance in learning mathematics, and lay a solid foundation for their future life and work.